Not all neighbors get along well. If you are lucky, you love yours or at least can tolerate them. However, there are many unlucky folks who must deal with problematic neighbors in many shapes and forms.
For example, maybe you have children, and your neighbors have a pool in the backyard. It is fenced but the gate lock is always broken. You have even caught your children trying to sneak into their pool and offered to pay for new locks. The neighbors just keep saying they will do it, and nothing changes. In other disputes, they might claim that part of your land is actually their property or vice versa. Perhaps their children keep coming into your yard and tearing it up despite your "No Trespassing" signs and fences. Maybe your neighbors constantly play music too loud and walk around intoxicated. In sum, there can be many reasons that neighbors do not get along. Some of these issues could be criminal matters, others civil or both. How do you know when an issue is worth pursuing?
Safety comes first
Safety comes first above all, so definitely call the police in such cases. It does not matter whose safety is at risk, yours, the neighbors', your kids or the neighbors' kids. A police presence is often enough to get neighbors to shape up, and if they do not, you at least have a record that you tried to remedy matters. Pursuing the matter in civil court can also be definitely worthwhile because it might prevent injuries and save lives.
If the dispute has cost you money, it is likely an issue worth pursuing. For example, if your neighbor bullies you to the point that you feel threatened and compelled to move as quickly as possible, you could potentially have a case in civil court if you had to sell your house at a loss. You may also be able to successfully recover against the party who sold you the house for failing to disclose pertinent information about the neighbors.